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自适应量子拓扑的动态拓扑变换驱动优化

Jincheng Zhang

Published Sep 7, 2026• 0 citations
Publisher

Abstract

This paper introduces a novel optimization algorithm based on adaptive quantum topology, leveraging the inherent structure of quantum systems to achieve precise parameter control and predictive capabilities. The algorithm utilizes a dynamic topology transformation process, which adjusts the topology of the system to guide the optimization process. This approach offers a fundamentally different methodology compared to traditional optimization techniques, particularly in the context of complex systems governed by quantum properties. We present a comprehensive analysis of the algorithm's design, demonstrating its effectiveness through theoretical analysis and preliminary experimental validation. The core mechanism centers around dynamically modifying the topology to influence the system's evolution, offering a robust framework for optimizing complex systems.

DOI
10.5281/zenodo.22619401

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Quantum topology, a burgeoning field of physics and mathematics, explores the topological properties of spacetime, offering potential for novel quantum technologies. This paper presents a novel algorithm, termed "Adaptive Quantum Topology Transformation" (AQTT), designed to dynamically adjust and transform complex systems based on inherent topological structures. AQTT leverages a self-adaptive framework to iteratively refine the system's topology, enhancing precision and enabling responsive adaptation to varying conditions. The core mechanism involves a series of meticulously controlled transformations guided by a sophisticated feedback loop, ensuring high-fidelity topological mappings. We demonstrate the efficacy of AQTT through theoretical analysis and preliminary experimental validation, showcasing its potential for addressing challenges in complex system modeling and control. The algorithm's ability to dynamically adjust topology represents a significant advancement in the field, offering a pathway towards robust and adaptable quantum systems.
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Quantum systems present unique challenges in optimization due to their inherent sensitivity to initial conditions and complex, often non-linear, dynamics. This paper presents a new optimization framework based on dynamic adaptive topology, a concept that aims to address these challenges by dynamically adjusting the system's topology during the optimization process. We introduce a method for identifying and exploiting the system's topology, enabling a more efficient and robust optimization process. The core mechanism involves constructing a dynamic topology representation of the system, enabling iterative adjustments and minimizing the influence of local optima. This approach has the potential to significantly improve the performance of various quantum systems, particularly those exhibiting complex dynamics. We demonstrate the effectiveness of this method through a series of simulations on benchmark problems, showcasing improvements in performance metrics compared to traditional optimization techniques. The research highlights the importance of dynamic topology in enhancing quantum system design and control.
Quantum computing offers the potential for exponentially faster computation compared to classical computing, driven by the ability to utilize quantum phenomena like superposition and entanglement. However, realizing this potential requires significant computational resources and precise control over quantum states. Parameter adjustment, the process of modifying the parameters of a quantum system to achieve a desired outcome, remains a critical challenge in quantum algorithm design. This paper introduces a novel algorithm, termed "Quantum Topology Optimization" (QTO), that leverages the inherent structure of quantum systems – specifically, topological structures – to dynamically adjust quantum parameters, ultimately leading to optimized computational results. We present a comprehensive theoretical framework and a preliminary implementation demonstrating the effectiveness of QTO in a simplified quantum circuit setting. The core mechanism hinges on automatically mapping and optimizing parameters based on the topological properties of the system, offering a significant departure from traditional parameter adjustment methods. This paper explores the potential of QTO to overcome the limitations of conventional approaches, paving the way for more efficient and robust quantum computation.